4400 Higher June 2005 Paper 4 Q15
15 A fan is shaped as a sector of a circle, radius 12 cm, with angle \(110^\circ\) at the centre.
Diagram NOT accurately drawn
(a) Calculate the area of the fan. (2)
Another fan is shaped as a sector of a circle, radius \(r\) cm, with angle \(120^\circ\) at the centre.
Diagram NOT accurately drawn
(b) Show that the total perimeter of this fan is \(\dfrac{2}{3}r(3 + \pi)\) cm. (3)
| Scheme | Marks |
|---|---|
| \(\pi \times 12^2 \times 110/360\) | M1 |
| 138(.2…) | A1 |
| (2) |
Notes
M1: Or \(\pi \times 12^2 \times 0.31\), Or \(\pi \times 12^2 \div 3.3\) or better
| Scheme | Marks |
|---|---|
| \(\frac{1}{3} \times 2\pi r\) or \(\frac{120}{360} \times 2\pi r\) seen | M1 |
| \(+\ 2r\) seen | M1 |
| \(\dfrac{2\pi r}{3} + 2r\) or \(\frac{2}{3}\pi r + 2r\) | A1 |
| (3) | |
| (5 marks) |
Notes
M1: Or equivalent explanation